Strong Perpendicular Magnetic Field Research Articles

Anisotropy in two-dimensional electronic quantum Hall systems at half-filled valence Landau levels

Strongly correlated electronic systems in two dimensions have constantly been a source of new discoveries. For example, the integer and fractional quantum Hall (QH) effects have emerged when such systems have been subjected to strong perpendicular magnetic fields. Recently, in the transitional regions between QH plateaus, strong magneto-transport anisotropies have been observed below ca. 100 mK. In this paper, we explain the emergence of broken rotational symmetry at half-filled valence Landau levels in terms of quantum liquid crystalline states with nematic order. Quantum Monte Carlo simulations indicate that while isotropic states are stable in the lowest and first excited Landau level, there are regions of instability towards liquid crystalline states in higher Landau levels. A possible connection of the recently discovered magneto-transport anisotropy in low magnetic fields and these liquid crystalline states is discussed.

Edges and interactions for graphene in quantum Hall states

We study the electronic structure near a graphene edge in a strong perpendicular magnetic field. In high Landau levels these edge states are similar in structure to those of standard two-dimensional electron gas systems (s-2DEG’s). The lowest Landau supports half as many edge states as those of higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to s-2DEG’s. The presence of both hole-like and electron-like edge states is shown to lead to the existence of a domain wall at the edge of an undoped graphene armchair edge when one considers the effect of quantum Hall ferromagnetism. The domain wall supports both collective and charged gapless excitations whose consequences for tunnelling experiments are discussed.

Multi-wavelength operation and vertical emission in THz quantum-cascade lasers

Multi-wavelength laser action in the terahertz (THz) region from a quantum cascade structure is demonstrated. Laser emission is obtained at 1.39 and 2.3 THz by using a structure based on a large single quantum well. A strong perpendicular magnetic field is employed to increase the gain and achieve laser action. In the second part of the work, a vertically emitting THz quantum cascade laser device that exploits an in-plane optical resonator based on a two-dimensional photonic crystal is demonstrated. Stable single mode vertical emission is reported. Simulations based on the block-iterative frequency-domain method on a plane wave basis account for the observed results.

Excitations from filled Landau levels in graphene

We consider graphene in a strong perpendicular magnetic field at zero temperature with an integral number of filled Landau levels and study the dispersion of single particle-hole excitations. We first analyze the two-body problem of a single Dirac electron and hole in a magnetic field interacting via Coulomb forces. We then turn to the many-body problem, where particle-hole symmetry and the existence of two valleys lead to a number of effects peculiar to graphene. We find that the coupling together of a large number of low-lying excitations leads to strong many-body corrections, which could be observed in inelastic light scattering or optical absorption. We also discuss in detail how the appearance of different branches in the exciton dispersion is sensitive to the number of filled spin and valley sublevels.

Influence of Coulomb scattering of electrons and holes between Landau levels on energy spectrum and collective properties of two-dimensional magnetoexcitons

This study is concerned with a two-dimensional electron–hole system in a strong perpendicular magnetic field with special attention devoted to the influence of the virtual quantum transitions of interacting particles between the Landau levels. It is shown that virtual quantum transitions of two Coulomb interacting particles from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their transition back to the lowest Landau levels in the second order of the perturbation theory result in indirect attraction between the particles supplementary to their Coulomb interaction. The influence of this indirect interaction on the chemical potential of the Bose–Einstein condensed magnetoexcitons and on the ground state energy of the metallic-type electron–hole liquid (EHL) is investigated in the Hartree–Fock approximation. The supplementary electron–electron and hole–hole interactions being averaged with direct pairing of operators increases the binding energy of magnetoexciton and the energy per pair in the EHL phase. The terms obtained in the exchange pairing of operators give rise to repulsion. Together with the Bogoliubov self-energy terms arising from the electron–hole supplementary interaction they both influence in the favor of BEC of magnetoexcitons with small momentum. The influence of the excited exciton bands on the energy spectrum and on the wave function of the lowest magnetoexciton band is studied in the second order of the perturbation theory. The BEC of magnetoexcitons in the superposition state is considered. The generalized Bogoliubov transformations, the BCS-type ground state wave function and the phase-space filling factors of the lowest and first excited Landau levels are determined.

Loss in a striated coated conductor

It is argued that a high-temperature coated conductor, despite being very thin, is describedby the same loss theory used for a typical low-temperature superconductor, except that ithas anisotropy. However, it is also argued that in both cases for a more completeunderstanding of the general loss problem the existence of a surface charge mustbe added to the standard theory. The hysteresis and coupling current loss for astriated coated conductor in a strong perpendicular ac magnetic field (but withoutnet transport current) is computed using the new theory. The total loss is thenobtained by adding a term due to eddy current loss in the substrate. The couplingcurrent loss is divided into a transverse and a longitudinal part, where the latter isneglected. The result is compared with measurements published by other authors.

Influence of excited Landau levels on a two-dimensional electron–hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron–hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose–Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron–hole liquid is investigated in the Hartree–Fock approximation. The coexistence of different phases is suggested.

Electrodeposition of Ordered Arrays of Multilayered Cu/Ni Nanowires by Dual Bath Technique

Abstract An ordered multilayered Cu/Ni nanowires array was electrodeposited into the pores of an anodic aluminum oxide(AAO) template, with layer thickness in the range of 3–100 nm. To avoid codeposition of Cu in the Ni layers, two separate Ni and Cu baths were used. Scanning electronic microscopy and transmission electron microscopy were used to characterize the morphology of Cu/Ni multilayered nanowires array. The results showed that the layer thicknesses are quite uniform and the multilayered structure is clear and regular. The nanowire diameter is about 100 nm, which corresponds to the pore size of the used AAO template. Selected-area electron diffraction (SAED) result demonstrates that those multilayered wires exhibit single crystal structures. Hysteresis curves for multilayered Cu/Ni nanowires array with the AAO membrane support were tested using vibrating sample magnetometer (VSM) at room temperature (293 K). It is found that the Cu/Ni nanowires arrays have strong perpendicular magnetic field anisotropy. When the magnetic field is perpendicular or parallel to the AAO template, the squareness ratio is 0.701 or 0.101, and the coercivity is 589 Oe or 202 Oe, respectively. The diameter and the layer thickness of Cu/Ni multilayered wires could be changed according to the demands by adjusting the technological parameters of anodization and electrodeposition.

Cooperative Recombination of a Quantized High-Density Electron-Hole Plasma in Semiconductor Quantum Wells

We investigate photoluminescence from a high-density electron-hole plasma in semiconductor quantum wells created via intense femtosecond excitation in a strong perpendicular magnetic field, a fully quantized and tunable system. At a critical magnetic field strength and excitation fluence, we observe a clear transition in the band-edge photoluminescence from omnidirectional output to a randomly directed but highly collimated beam. In addition, changes in the linewidth, carrier density, and magnetic field scaling of the photoluminescence spectral features correlate precisely with the onset of random directionality, indicative of cooperative recombination from a high-density population of free carriers in a semiconductor environment.

Quantum Hall droplet at excitonic filling factorν=2in a self-assembled quantum dot

We present a theory of excitonic quantum Hall droplet (EXQHD) at filling factor $\ensuremath{\nu}=2$ in a self-assembled quantum dot (SAD) subject to strong perpendicular magnetic field $B$. Using exact diagonalization technique we determine the ground and excited states, the stability against spin flips, and the optical emission spectrum of the $\ensuremath{\nu}=2$ EXQHDs. In contrast with one-component electronic droplets, the singlet-singlet $\ensuremath{\nu}=2$ EXQHD is found to be intrinsically correlated, and stable even in high magnetic fields due to the neutrality of exciton. The characteristic spin related emission spectrum and its magnetic field evolution from the EXQHD are predicted.

Replica study of pinned bubble crystals

In higher Landau levels ($N>1$), the ground state of the two-dimensional electron gas in a strong perpendicular magnetic field evolves from a Wigner crystal for small filling $\nu $ of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as $\nu $ increases, to a modulated stripe state near $\nu =0.5$. In this work, we compute the frequency-dependent longitudinal conductivity $% \sigma_{xx}(\omega) $ of the Wigner and bubble crystal states in the presence of disorder. We apply an elastic theory to the crystal states which is characterized by a shear and a bulk modulus. We obtain both moduli from the microscopic time-dependent Hartree-Fock approximation. We then use the replica and Gaussian variational methods to handle the effects of disorder. Within the semiclassical approximation we get the dynamical conductivity as well as the pinning frequency as functions of the Landau level filling factor and compare our results with recent microwave experiments.

Control of Optical Gain in the Active Region of Quantum Cascade Laser by Strong Perpendicular Magnetic Field

The optical gain in the active region of quantum cascade laser in an external magnetic field is analyzed. When the magnetic field is applied in the direction perpendicular to the plane of the layers, electron dispersion is broken into series of discrete Landau levels. This additional confinement strongly modifies the lifetime of electrons in the upper state of the laser transition, which is controlled by electron-phonon scattering. Landau levels are magnetically tuneable and, depending on their configuration, phonon emission is either inhibited or resonantly enhanced. This translates into a strong modulation of the population inversion, and consequently of the optical gain by varying the magnetic field. Numerical results are presented for a structure previously considered by Smirnov et al. [Phys. Rev B 66 (2002) 125317] which is designed to emit radiation at λ~11.4µm, with the magnetic field varied in the range 10-60T. The effects of band nonparabolicity are taken into account in this model.

Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

A previous work [Shen, Ma, Xie, and Zhang, Phys. Rev. Lett. 92, 256603 (2004)] on two-dimensional quantum wells with Rashba type spin-orbit interaction under a strong perpendicular magnetic field is generalized to include the Dresselhaus coupling. The Rashba coupling and the Dresselhaus coupling interplay with the Zeeman effect in opposing ways. The former tends to produce a resonant spin Hall effect at certain magnetic fields while the latter suppresses it. Due to the resonant spin Hall effect, the spin Hall current is highly nonohmic at low temperatures. The condition for the resonant spin Hall conductance in the presence of both Rashba and Dresselhaus couplings is derived using a perturbation method. In the presence of disorder, we argue that the resonant spin Hall conductance occurs when the two Zeeman split extended states near the Fermi level become degenerate due to the Rashba coupling, and that the quantized charge Hall conductance changes by $2{e}^{2}∕h$ instead of ${e}^{2}∕h$ as the magnetic field changes through the resonant field.

Charge-density response function of two-dimensional electron systems in a magnetic field

We examine charge density excitations in two-dimensional electron systems in a strong perpendicular magnetic field. Our theoretical framework is the extended random-phase approximation (extended RPA, ERPA), which takes into account all the second-order self-energies of particle-hole propagators. Our results are different from the RPA response functions qualitatively, and are consistent with recent empirical findings. We explain our results in detail in connection with two-particle-two-hole degrees of freedom and the Kohn theorem.

Rashba spin precession in quantum-Hall edge channels

Quasi-one-dimensional edge channels are formed at the boundary of a two-dimensional electron system subject to a strong perpendicular magnetic field. We consider the effect of Rashba spin-orbit coupling, induced by structural inversion asymmetry, on their electronic and transport properties. Both our analytical and numerical results show that spin-split quantum-Hall edge channels exhibit properties analogous to that of Rashba-split quantum wires. Suppressed backscattering and a long spin lifetime make these edge channels an ideal system for observing voltage-controlled spin precession. Based on the latter, we propose a magnetless spin-dependent electron interferometer.

The Controlled Manipulation of Parameters of the Quantum Antidot

The electron motion in a strong perpendicular magnetic field close to the impenetrable obstacle is considered by the semi-classical and quantum points of view. We investigated an influence of a shape of the forbidden region to the formation of the plateaux in the one electron energy spectrum and transmissions between dot and antidot states. In the semi-classical regime electrons can be treated as charged particles with well-defined trajectories pinned to the potential wall. This approach, combined with singular equation technique in quantum calculations, has given us a possibility to investigate stripe-shaped and bow-shaped antidots with sharp edges and to find a way for controlled manipulation of the parameters of systems with an effort to get desired physical properties.

Coexistence of two Bose–Einstein condensates of two-dimensional magnetoexcitons. Exciton-plasmon collective elementary excitations

Possibility of the Bose–Einstein condensation of magnetic excitons in an ideal two-dimensional system in a strong perpendicular magnetic field is investigated theoretically taking into account the influence of virtual transitions to the excited Landau levels and Anderson-type coherent excited states. It was understood, that the Bose–Einstein condensed (BEC-ed) magnetoexcitons with considerable wave vector K and motional dipole moment Kl 2, where l is the magnetic length, can form the droplets of the metastable dielectric liquid phase, whereas the BEC-ed magnetoexcitons with K =0 can form a stable degenerate Bose-gas surrounding the droplet. We have shown that collective elementary excitations of the BEC of excitons are mixed with plasma oscillations of the electron–hole system in the presence of strong perpendicular magnetic field. Their mutual influence is determined by the coherence factor and essentially depends on the condensate wave vector K.

THE INTERRELATION BETWEEN INCOMPRESSIBLE STRIPS AND QUANTIZED HALL PLATEAUS

We study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with integer values of local Landau-level filling factor exist for finite intervals of the magnetic field strength B. Within an essentially local conductivity model, we find that the current density in these B intervals is confined to the incompressible strips of vanishing local longitudinal resistivity. This leads to vanishing longitudinal and exactly quantized Hall resistance, and to a nice agreement of the calculated Hall potential profiles with the measured ones.

Non-linear ring currents: effect of strong magnetic fields on π-electron circulation

Finite-field calculations of non-linear induced current density in representative [4 n + 2] and [4 n] π systems, benzene and flat cyclooctatetraene (COT), show that a strong uniform perpendicular magnetic field enhances benzene π-diatropicity and decreases COT π-paratropicity. The non-linear current is stronger by two orders of magnitude in COT, but still small: at 1 a 0 height and in a field of 25 T, third-order effects contribute −5 ppm to the first-order π ring current. Classical arguments based on radial contraction of charge density rationalise the non-linear response of benzene, but that of COT depends on a specific orbital-rotation effect, characteristic of paratropic π systems.

Photoluminescence rings in a Corbino disk at quantizing magnetic fields

Spatially resolved photoluminescence of modulation doped AlGaAs/GaAs heterojunction was investigated in a sample of Corbino disk geometry subject to strong perpendicular magnetic fields. Significant spatial modulation of the photoluminescence was observed in form of one or more concentric rings which travelled across the sample when the magnetic field strength was varied. A topology of the observed structure excludes the possibility of being a trace of an external current. The effect is attributed to formation of compressible and incompressible stripes in a 2DEG density gradient across the sample.